Time Reborn

Lee Smolin’s new book, Time Reborn, is out today. For more about the ideas in the book, see video of a talk here, and an interview here.

While I mostly vehemently agreed with what Smolin had to say in his last book, The Trouble With Physics, I find myself equally vehemently in disagreement with this one. On some of the topics covered, I’m indifferent to his arguments mostly as a matter of taste. While my views on human society are likely similar to Smolin’s, I’ve never found the scientific insights of fundamental mathematics or physics to have anything significant to tell me about this part of life. Similarly, while I’ve spent some time studying philosophy, I’ve mostly found this of little help in gaining deeper understanding of math or physics. Others though have a very different experience than me, and I’m not about to argue against people looking for enlightenment wherever they happen to find it.

On some of the scientific issues dealt with in the book, again I’m mostly just indifferent. Smolin accurately explains how the lack of predictivity makes typical multiverse models empty, but I’m not convinced that his favored alternative (“cosmological natural selection”) does much better. While I understand well the human appeal of wondering about what came before the big bang, I’ve yet to see any specific models of this that carry enough explanatory power about anything to make them particularly attractive or interesting.

Many of the ideas Smolin is arguing for are clearly labeled as what they are: speculative challenges from a very much minority point of view to some of the received wisdom of this kind of science. Unfortunately, parts of his argument that are most problematic are ones which are in danger of becoming the new received wisdom of the subject. The refusal to admit the failure of the idea of string/M-theory unification has left many of our most prominent theorists pushing the idea that fundamental physics is based on some new and very different degrees of freedom, with dynamics that just happens to be too complicated to allow them to find vindication by seeing how the Standard Model emerges at low energies. For his own reasons, Smolin signs on to a version of this point of view, writing:

I’m inclined to believe that just about everything we now think is fundamental will also eventually be understood as approximate and emergent: gravity and the laws of Newton and Einstein that govern it, the laws of quantum mechanics, even space itself…

A large part of the elegance of general relativity and the Standard Model is explained by understanding them as effective theories. The beauty is a consequence of their being effective and approximate. Simplicity and beauty, then, are the signs not of truth, but of a well-constructed approximate model of a limited domain of phenomena.

The notion of an effective theory represents a maturing of the profession of elementary-particle theory. Our young, romantic selves dreamed we had the fundamental laws of nature in our hands. After working with the Standard Model for several decades, we are now simultaneously more confident that it’s correct within the limited domain in which it has been tested and less confident of its extendability outside that domain.

This notion that the SM is “just an effective theory”, with its fascinating and deep mathematical structures nothing but an artifact of low-energy approximation has become the reigning ideology of the last few decades. One impetus for this has been string/M-theory, with its conjectured very different physics at short distances. This has been put together with our modern understanding of renormalization, according to which non-renormalizable theories make perfect sense as effective theories. The argument is then made that this is all there is to the SM, neglecting to note that to a large degree the SM couplings are asymptotically free, meaning that (most of) the quantized geometric degrees of freedom make perfectly good sense at all energy scales.

Smolin’s view that the recent history of particle physics makes us “less confident of its [the SM’s] extendability outside that domain [where it has been tested]” is one I strongly disagree with. Despite endless “naturalness” and “fine-tuning” predictions based on the “nothing but an effective theory” argument, the SM has not only been vindicated at the LHC over a large new energy range, but the discovery of the Higgs has shown it to have just the right characteristics to make perfectly good sense up to extremely high energies, far beyond anything we can test.

I’ve been teaching a course this past year on quantum mechanics for mathematicians, emphasizing the role of Lie groups, unitary representations and symmetries in providing not only useful calculational methods, but governing the underlying structure of the theory. Smolin argues instead that, based on Leibniz’s “identity of the indiscernibles”, symmetries cannot be fundamental (although a footnote says this doesn’t apply to gauge symmetries):

Symmetries are common in all the physical theories we know. Several of the most useful tools in the physicist’s toolbox exploit the presence of symmetries. Yet if Leibniz’s principles are right, they must not be fundamental.

This applies to the very structure of quantum mechanics:

Quantum mechanics, too, is likely an approximation to a more fundamental theory.

since it is linear, and he bets thus just a linear approximation to some fundamentally non-linear theory. Again, mathematical simplicity is seen as an artifact of approximation, not indication of something fundamental.

Smolin ends with a vision that is pretty much the exact opposite of mine, one with a vastly diminished role for mathematics in understanding the nature of reality:

The most radical suggestion arising from this direction of thought is the insistence on the reality of the present moment and, beyond that, the principle that all that is real is so in the present moment. To the extent that this is a fruitful idea, physics can no longer be understood as the search for a precisely identical mathematical double of the universe. That dream must be seen now as a metaphysical fantasy that may have inspired generations of theorists but is now blocking the path to further progress. Mathematics will continue to be a handmaiden to science, but she can no longer be the Queen.

Unfortunately it seems possible that Smolin’s arguments about mathematics will resonate well with the current backlash against sophisticated mathematics that one sees at many physics departments in the wake of the failure of string theory. In a footnote he explicitly argues that the problem with string theory was too much symmetry:

Indeed, we see from the example of string theory that the more symmetry a theory has, the less its explanatory power.

I don’t understand this argument at all. The problems with string theory are something I’ve written about endlessly here, but too much symmetry is not one of these problems.

Smolin has been quite right to point out in recent years that fundamental physical theory is in a state of crisis, but I think his diagnosis in this book is the wrong one. Abandoning the search for a more powerful mathematical understanding of the world because the huge success of this in the past has made further progress more difficult is the wrong lesson to draw from recent failures (the nature of which he lucidly described in his previous book).

My own interpretation of the history of the Standard Model is that progress came not from finding more, larger symmetries, but from a deeper appreciation of the various ways in which gauge symmetry could be realized (spontaneous symmetry breaking, confinement, asymptotic freedom). The arrival of string theory pushed the study of gauge symmetry into the background, and these days one often hears arguments against its fundamental nature, such as this one from Arkani-Hamed

What’s as a misnomer called gauge symmetry, whose beauty is extolled at length in all the textbooks on the subject, is completely garbage. It’s completely content free, there’s nothing to it.

Smolin’s arguments against the fundamental nature of symmetries, even if gauge symmetry is let off the hook in a footnote, just reinforce some of the attitudes at the root of our present-day crisis. The problems that remain in fundamental theory are difficult, but denigrating now the powerful ideas that have led to success in the past won’t help find a way forward.

83 Responses to Time Reborn

Einstein-Leopold’s book, the “Evolution of Physics” has been my favorite popular book (not because it is the best written popular description but because it contains Einstein’s thinking in his own words) — as Neils H. Abel said, study the words written by the masters themselves, not their pupils. I have read that book a gazillion times. Smolin’s book “The Trouble with Physics” is the other popular book I have read multiple times and the page that stumps me is p.257 and its statements about time and Smolin’s not being happy with the simple diagram he drew there.

Now Smolin has a whole book on time! Well, it is not available at Indian online stores so have just ordered from Amazon, where they really loot you on international shipping. Jeff Bezos ships free in the USA, rips-off the rest of the world. Maybe I could have saved some money by searching places like Ebay etc but that takes time. I plotted a money-time graph and realized I really don’t know what time is! Can’t wait to find out 😉

What I admire most about Smolin is that he one of the two professors who gets special mention on my favorite site about special relativity: physicsnext.org!

Chris,
Good question. It does go the the main problem of time. Whether the events are the denominator and the present the numerator, with this eternally existing fabric of spacetime, or it is the present as the denominator and the events the numerator, so that it is just one constantly changing present.

Many thanks, that is an excellent question. The importance of shape dynamics, the development I describe in Chapter 14 of Time Reborn, is exactly that it explains how time dilation and other phenomena of special relativity can be made consistent with a real global time. To put this briefly, shape dynamics has a gauge symmetry under local scalings of volume. But if you shrink the volume a clock occupies you make it tick faster because clocks are physical devices and their size affects their rates. This is evident in models of clocks called light clocks in which what ticks is a photon bouncing back and forth between two mirrors. Hence you can trade a relativity of time with fixed sizes for a relativity of size with fixed times. This leads to an equivalence with general relativity and, as Barbour and collaborators have shown in detail, there emerges all the phenomena of special and general relativity. How this works in detail requires of course a bit more technicalities.

Thanks for your thoughts on irreversibility. This issue is the subject of work in progress with Marina Cortes, so please look for papers to appear.

Dear srp,

I’m not sure how you got the impression momenta run backwards in time in the model I discussed in that talk; all momenta run from past events to future events.

Dear Marcus,

Many thanks for those references. I agree that these NS’s have central values of their measured masses larger than 2 solar masses, but the error bars are large enough this is consistent with 2. But these make me hopeful that soon a NS may be discovered with a mass definitively above 2 solar masses. I would not be unhappy to be able to write a paper saying that a prediction of cosmological natural selection has been falsified because this supports my key point that it is more scientific to posit evolving laws than timeless laws.

Dear Nathalie,

I understand that you are concerned that by discussing philosophical and methodological issues in public we may mislead laypeople to confuse ideas in progress with settled facts. This is a great concern of mine as well and I don’t believe I was doing that at PI-because I made it clear more than once that I was not addressing the normal practice of physics but only its extension to a theory of the whole universe. But I do share your general concern and if you have any concrete suggestions I’d be very happy to incorporate them into my future public talks. Meanwhile I would very much appreciate it if you would look carefully at the book and/or the talk and understand that I am not attacking mathematics in general or saying all physics is wrong etc. I don’t mind at all if my argument is criticized but it is helpful when the criticism is directed at what I am actually saying rather than being based a misunderstanding.

In re … “. . . you can trade a relativity of time with fixed sizes for a relativity of size with fixed times. This leads to an equivalence with general relativity and, as Barbour and collaborators have shown in detail, there emerges all the phenomena of special and general relativity.”

Except that Barbour et al are compelled to trade the geometry of spacetime (GR) for a geometry of space without temporal causality. I can’t see how this view is at all compatible with yours, if you want a model in which time is physically real.

On the other hand, I find no conflict between the conventional view of general relativity which describes a universe “finite and unbounded” — taken to mean bounded in time at the singularity of creation and unbounded in space by continuous positive curvature — and a universe finite in space and unbounded in time. I think that would preserve spacetime as physically real, as well as the physical evolution of time itself. I am skeptical of assigning a causal role to geometries and symmetries — however dynamic we imagine them to be — independent of a guiding physical principle.

There is real time with temporal causality in shape dynamics, at least at the classical level, and there is a beautiful recent paper about this by Barbour, Koslowski and Mercati, http://arxiv.org/abs/1302.6264.

BTW, anyone who claims that he has read the book in these few days – should reconsider. Peter included, although I suspect that he (like Bee) had access to the volume beforehand. This is not a book to be read in four days. Be patient and give it the time and thought it deserves.

Lee,
Thank you for adding that response because quite honestly, I didn’t connect the dots between your GR application of shape dynamics (time is universal and size is relative) and the other statements about SR in that same chapter. After rereading chapter 14 along with Barbour’s paper from the link you provided (I assume Barbour’s dimensionless time variable and your real preferred global time mean the same thing) I sort of get it now – but I don’t know if I agree with it.

On p. 170, you say: “This global notion of time implies that at each event in space and time there is a preferred observer whose clock measures its passage.” Then, according to shape dynamics, you could argue that both GR and SR time dilation effects would produce “deviations” from the preferred global time because of the “size relativity” experienced in each. But, even if you consider a particular object to be at absolute or preferred rest, it is still in some other object’s gravitational field even if by just a trace, and will have a miniscule deviation from the true global time. If I have that right, then doesn’t real global time become a theoretical value that is not experienced by anything in the universe?

Also, how closely does the “size relativity” in shape dynamics relate to the length contraction hypothesis in special relativity? I want to make sure I understand your comment in your earlier post along with another statement of yours explaining Barbour’s position from chapter 14: “Shrink everything in one place and somewhere else, enlarge everything by the same amount.” I ask because according to SR, length contraction, along with time dilation is considered to be a reciprocal effect from the perspective of both the observer and traveler. And the “shrink everything/enlarge everything” statement seems to hint at an inverse proportion rather than reciprocal effect. Unless the shrinking and enlarging doesn’t necessarily apply to two clocks running at different rates? Can you clarify?
Thanks again

John M. – Thanks, hope all is well. I noticed the early time of your post. I envy you. I wish my brain worked in any capacity before 6:00 am.

I’m curious to know if the book contains this Youtube link to a short conversation between Richard Feynman and Fred Hoyle recorded around 1972:http://www.youtube.com/watch?v=uNOghidK2TY
The clip is 9 minutes and 35 seconds long but if you are in a hurry you can skip the first 8 or 9 minutes.
Relaxed conversation at a Yorkshire pub. If you start around minute 8:00 you get some of the atmosphere. But the main thing is in the last 35 seconds of the clip.

A Caltech archive has the text of what Feynman says there:http://calteches.library.caltech.edu/35/2/PointofView.htm
Scroll 3/5 of the way down the page.
“It is interesting that in many other sciences there is a historical question, like in geology – the question of how did the earth evolve to the present condition. In biology – how did the various species evolve to get to be the way they are? But the one field which has not admitted any evolutionary question is physics. Here are the laws, we say. Here are the laws today. How did they get that way? – we don’t even think of it that way. We think: It has always been like that, the same laws – and we try to explain the universe that way. So it might turn out that they are not the same all the time and that there is a historical, evolutionary question.”

There seem to be two problems being addressed: the Problem of Time, and the Problem of Laws. (Why these laws? How did they come about?) The Barbour Koslowski Mercati paper Lee mentioned solves the first–the problem of time–in the shape dynamics context, but does not address the second.

I have a few questions:
1) Does the reality of time imply that (total) information is always being created at a fundamental level (and thus non-unitary)?

2) I do not understand your statement that since the universe includes everything, there could be no eternal mathematical truths or laws outside of the universe that nature can correspond to.
But, mathematical laws need not be physically lying outside of the universe – they are mental products, and thus of a different category from the physical universe. It is wrong to say that they are outside of the universe.

3) Maybe the reality of time depends on our viewpoint, whether it is from inside or outside? For an observer inside the universe, using tools defined entirely from inside, time can be shown as real. But if we see from outside (God’s eye view) like Newton’s theory, all time is equal.

Daniel, about your question (2) I don’t remember Lee saying what you have him saying there. A handy way of distinguishing a mathematical law from a physical law is that a law of physics *could be different*. It’s a key distinction.

With a law of physics one can reasonably ask “why is it this way rather than that?” because there is empirical content. You rightly point out that mathematical truths are of a different sort. Mathematics is an evolving human language within which true statements are deduced non-empirically from sets of axioms.

Have a look at slide #5 of PIRSA 13020146. It’s a talk Lee gave *about the book* in the Quantum Foundations seminar at Perimeter. You can download the slides PDF and review the logical outline of the talk after watching the video. Slide 5 gives a couple of concise principles that the rest of the talk (and I believe the core argument in the book) is based on.

The first principle shown (labeled PSR) is carefully worded so that it applies to laws of physics and not to pure math.
I can’t recommend watching the February Quantum Foundations seminar talk too highly. It’s an immediately available clear concise presentation of the logical argument at the heart of the book.http://pirsa.org/13020146/

My kibitzing like this is not meant to detract. Hopefully Lee will provide a more complete authoritative response later.

Having read the Julian et al paper you linked, I want to echo Chris’s comment “(I assume Barbour’s dimensionless time variable and your real preferred global time mean the same thing) I sort of get it now – but I don’t know if I agree with it.”

Except that I’m not sure that I even sort of get it. A dimensionless time is dimensionless spacetime. And I don’t see how shape without geometry differs from change without differentiation. We can believe it, philosophically — yet how can we hope to demonstrate that such is fundamentally “physically real” in Einstein’s terms, i.e. ” … independent in its properties, having a physical effect but not itself influenced by physical conditions.” (from The Meaning of Relativity, 1956.)

Minkowski spacetime and general relativity may be old hat, and perhaps I’m a Philistine, yet I cannot get my mind around a more fundamental background-free starting point for energy exchange between bosonic and fermionic particle properties.

Tom, I don’t see how you come to your stated assumption: “I assume Barbour’s dimensionless time variable and your real preferred global time mean the same thing.”
They seem quite different animals to me! Surely they are constructed in entirely different ways. Can you clue me in to your thought process?

What Lee said earlier in these comments was: “The importance of shape dynamics, the development I describe in Chapter 14 of Time Reborn, is exactly that it explains how time dilation and other phenomena of special relativity can be made consistent with a real global time. To put this briefly, shape dynamics has a gauge symmetry under local scalings of volume…”

I bolded the article “a” because it as much as says that they are NOT the same global time, as far as the speaker knows. The point seems to be that there exists at least one global time which is consistent with such and such phenomena.

Alain Connes and Carlo Rovelli have also proposed a global time, based on the Tomita flow on star algebras—theirs seems quite different from either of the others although agreement is possible where applicable in special cases: all might be found to agree with the global time of Friedman equation cosmology in that model. Anyway a global preferred time is not such a rare beast that whenever you see two of them you must assume they are the same. But maybe you have reasons to equate them and I’m being too cautious. 🙂

Sorry to add confusion, Marcus. I didn’t say it. Chris Kennedy said it. I haven’t even gotten to chapter 14 of Lee’s book. The Barbour et al paper I did read, however, and I cannot reconcile what I know that Lee has said in the past with Julian’s concept of shape dynamics and the (nonphysical) role of time.

I thought Lee was a relativist, albeit with an enhanced physical role for time and the possible inclusion of nonlocal hidden variables (the class of theories in fact, to which string theory belongs).

I think global time is a pretty slippery concept. I’m compelled to agree with George Ellis that without a well defined local arrow of time, there is no life — even further though, I think, no matter — whether baryonic or dark. The more I look at these causal structure theories, the more convinced I become that physically real spacetime and general relativity still hold the key to theoretical completeness.

Marcus,
I assumed it, but wasn’t 100% sure, so I threw it in there in case I needed to be corrected. However, I believe all of the the comments below that are pretty consistent with questioning preferred global time, so I hope Lee comments on the issues I’ve raised.

1) I would argue that there must be a cosmological theory which quantum mechanics approximates for small subsystems of the universe, which would have an evolution law which is expressed in a language not that of quantum theory. This would of course conserve probability but might not be expressed as unitary evolution on a Hilbert space.

2) If you think mathematical objects are “Mental products” you are not a platonist and you believe mathematical objects are within the universe as are the brains or minds that created them. I claim that mathematics can provide excellent models of the records of past observations of subsystems of the universe. But all such models, describing subsystems, involve truncations and are hence incomplete. I however argue in the book that they cannot be completed by extending the model to encompass the universe as a whole. The core of the argument of the book, which I won’t repeat here is why this cannot be done.

3) I deny there is any scientific sense to a description of the universe from outside of it, for reasons given in detail in the book.

Tom,

I don’t mean to imply that shape dynamics gives a view of real time in all the aspects I mean that, which are specified on page xiv. What shape dynamics does do is show how the existence of a preferred global time, in which the spacetime evolves through hamiltonian evolution, is compatible with relativistic causality.

Also, Barbour’s previous arguments that time disappears in quantum cosmology are not the same as or necessarily relevant to shape dynamics, which is so far only understood at a classical level.

Chris,

It is important to distinguish special relativity, where the lorentz group describes a global symmetry from general relativity, where the many fingered time, or spacetime diffeomorphisms describe a gauge symmetry. Shape dynamics is a reformulation of the latter in which the many fingered time gauge symmetry is replaced by a local scale gauge symmetry. To address your question in detail of exactly how time dilation arises in shape dynamics is possible-because SD is equivalent too GR, but a technical exercise as global symmetries are already a subtle issue in general relativity.

Thank you — that’s a relief. If I am to understand shape dynamics in a classical framework, I can also grasp preferred global time as continuous, with classical time reverse symmetry. I’m afraid this discussion is getting a bit ahead of my reading the book — need to catch up!

Lee,
I guess after learning what little I know about shape dynamics, I will limit my observations to its explanation of time dilation in Special Relativity.
The clarification I’m looking for is whether the relativity of size correlates with the reciprocal length contraction proposed for SR during relative inertial motion. This is an extremely important question. By the way, in certain relativity writings, “reciprocal” refers to equal but identical, which is how I use it here. In other words, I see the moving ship contract, and the moving ship sees the space it’s traveling in contract. SR also says that I will see the ship’s clock run slower while the people on the ship see mine run slower as well.
I am asking this because you said in your book that: “SD achieves an accord between the experimental success of the principle of relativity and the need for a global time…..”
Any sane person who has studied relativity would have to admit that all of the experimental evidence certainly shows that time dilation during motion and proximity to mass is a real phenomenon. But there are a lot of sane people who are not aware that certain physical evidence (GPS system) shows that the time dilating effect is not reciprocal during relative motion. If the satellite clocks are running slower from the perspective of the ground (having already adjusted for the gravitational effect) and the satellite sees the ground clock running slower than itself, there is no compensation that can be applied to either clock (or both) to get them to run in sync from both perspectives simultaneously – but yet they do and the system works quite well.
So, if shape dynamics is not reliant on the framework of these reciprocal effects in SR, then I would say it has a chance, but if it is reliant on that aspect of SR, then I would say it is in serious trouble.
I think I speak for all of the questioners here when I say we appreciate your continued participation in this conversation. “Time” is an important issue that never seems to get the attention it deserves.

What I wanted to say is that even if there is nothing outside the universe, this does not imply that there is not a realm of mathematical truths where nature corresponds to.
Platonic realm is conceptual, and not something physically lying outside the universe. So its existence does not contradict the fact that there is nothing outside the universe.
“Outside” is a relationship between two physical objects.

It is easy enough to represent global Poincaré symmetry in Shape Dynamics, as long as you have (as Lee mentions), a flat ansatz*. The way this comes about (at least mathematically), is that due to the high geometric degeneracy, there is a family of exactly 4 time directions which cannot be traded for conformal symmetry in the construction of Shape Dynamics. These directions correspond to time translation and boosts, or alternatively, to Minkowski and Rindler. In this degenerate case, quite unexpectedly, the Shape Dynamics algebra of the 4 respective Hamiltonians (supplemented with the isometries of flat 3-space) form the Poincaré algebra.** So I would say that at least in the way its been derived it does not depend on the reciprocity you mention. The appearance of a singled out time direction, once the trading of symmetries is complete, would appear only when you add inhomogeneities to the Universe.

* (in fact all you need is a spatial spherically symmetric ansatz in asymptotically flat SD with no boundary mass charge)

** I should mention that this algebra is already represented as a boundary charge algebra in this circumstance, but the charges are slightly different than in GR, see http://arxiv.org/abs/1212.1755 .

To anyone who might know:
In Barbour’s book “The end of time” he talks about the timeless formulation of quantum mechanics. I only read the book once so far and couldn’t understand if it is working or just how he imagines it to work, in contrast to Newtonian mechanics, SR and GR, where I understood the construction.
So is there a mathematical formulation of timeless QM? And could You please point out a (some) paper(s) on this?
Thank You,
Tobias

I’ve just finished reading the book, and I have questions. I don’t know if Lee Smolin will see these, but anyone is welcome to answer.

1. In Cosmological Natural Selection (CNS) you need to get Big Bangs to come from Black Holes, but obviously the theory of if/how this happens needs much more development. In particular you don’t know what it takes for a Black Hole to make a good baby universe, not just with good constants, but also with the special initial conditions like our own Big Bang, and still following GR and QT to the extent that there’s a choice, and so on. Given this uncertainty in the theory, what does that imply for prediction and falsifiability in CNS? It might be better for a universe to have fewer fitter offspring (just as in biology), so just maximizing the number of Black Holes cannot be a necessary requirement of CNS.

2. If there is a to be a global time, then it is a totally ordered set (of “instants”). What does this sequence of instants look like? The integers, the rationals, the reals, something else? Or is this a case where mathematics cannot fully capture the physics? Or are the “instants” actually blurred out and uncertain, and least by the order of one Planck time?

3. How strong is the argument that “real time implies global time” anyway? What’s wrong with real time (now is real, past and future is not) while still having multi-fingered time, as long as neighboring patches of space keep up with each other? What if you had two or more totally causally disconnected universes: would they need to share a global notion of simultaneity with each other? Maybe I’m being dense but I’m not seeing it as settled that there either must be a global time, or no (real) time at all.

4. If there is to be a global time, does it necessarily have to be one picked out by the shape dynamics argument? There’s lots of ways to map a partial order to a total order? How do you choose which is the “true global time” (or was this just an in principle argument about what might be the true global time)?

5. What viable proposals are there where GR and QT are not taken to be absolutely true, but where some dynamical process tends to push violations of these laws towards zero? (This is meant to be analogous to various feedback mechanisms in a living organism, on a faster timescale than evolution.) As a possible very specific example, take a spacetime, find the global time t picked out by the shape dynamics argument, then reformulate GR, by describing how a spacelike slice S(t) at constant time t, with appropriate fields, and satisfying appropriate conditions, would evolve as a function of t. But then extend these dynamics so that they can be applied to an arbitrary spacelike slice, and you want it to be that as you evolve it into the future as a function of a time parameter t, that the future spacelike slices converege to the spacelike slices you get from the shape dynamics argument. Is something like this done?

6. Is there a connection between “constant mean curvature slicing” (Note 10 of Chapter 14) and Penrose’s Weyl curvature hypothesis?

7. As an idea of where QT could break down, what do you think of Penrose’s proposal that the laws of physics are such that a quantum superposition of macroscopically different ditributions of mass/energy will not occur, (i.e. despite QT, things won’t deviate too far from classical GR, except possibly near singularities)?

8. What does it mean for space to not be real? It seems to be pretty much a 3-dimensional sheet of stuff to me even when it’s “empty” (and even if it sometimes looks like an arbitrary graph, I’d still just call that unfamilar, not unreal)?

9. Any idea why nature “tricks” us into thinking that there are laws with (sometimes broken) symmetries, when in reality the symmetries were never there to start with (so there’s no symmetry to break)? You say there is a global time, preferred inertial observers, and so on. So for example local Lorentz symmetry is not imposed by any law, but it looks true. Is this something amazing to be explained, and what is the explanation (perhaps some dynamical process as in 5. above might work)?

Sorry for the delayed response to your excellent questions. btw I am soon to be launching a blog to discuss questions like these with readers. To answer yours:

1) To make the theory predictive in the absence of a detailed model of a bounce I assumed that each black hole yields a single viable universe. Obviously you could complicate the model in many different ways and one could also try to take advantage of progress in quantum gravity since then to model the bounce.

2) This is a good question.

3) What do you mean that they keep up with each other? Isn’t that a global time? But of course its not settled, I give several independent arguments, please disagree specifically with them.

4) Of course, but SD shows a global time can be compatible with experimental tests of SR and GR. There could of course be other choices. I mention several in the notes.

5) This is a good research program to pursue.

6) No

7) Its an interesting hypothesis to investigate.

8) The point is that an arbitrary graph with some graph metric on it does not embed isometrically in a low dimensional space

It doesn’t matter whether you call a proposed governing principle (by which known regularities could have developed) a description of “how Nature works” or a “meta-law” or simply a more basic law of Nature.

What seems to matter is that the body of physical law has become seemingly over-intricate and arbitrary. This makes for a general desire for one deeper law that explains where all the previous laws “came from”, and Smolin presents a case, based on many interesting arguments, that the most promising area to search is in the direction of historical/evolutionary principles.

A frivolous paraphrase of one example he presents might be “Nature tends to run in ruts it made itself earlier” or “being the universe is habit forming”. This harks back to the examples of biological evolution and the development of English Common Law by the accumulation of precedent. It seems to me that any such principle would have to be formulated with the help of some new mathematical language before it could be used predictively and tested. And it would itself be outside of the evolutionary process.
Any description of how Nature works is going to have some postulate or rule that does not itself evolve and which is not reciprocally acted upon by what it guides.
So the main idea is not to reject timeless law, expressed in partly mathematical language, it is to find more elegant description and more economical explanation.

And the case is made that this must involve the temporal development of previously recognized regularities–so it looks like we must accept (I think he would say) the idea of a preferred global time slicing of events.

A message for Lee: The one area that really raises questions for me is precedence: how and why would that become established, causing universe wide behaviour under similar circumstances to be consistent and thus create a “law” ?

David, I hope Lee responds to your question, but would like to observe that I addressed that issue. Precedence, if you can pull off a workable formulation, is just a more elegant basic law of nature. It is a single law that might be capable of explaining how the previously recognized physical laws arose. It isn’t any more crazy to assume precedence (if you can formulate it) than any other fundamental law. How does an electron know it’s and electron and that it should behave such-and-so way? Indeed precedence sounds potentially LESS preposterous to me than other fundamental laws—it is just that one has gotten used to it that one doesn’t notice how crazy it is that matter should behave according to the Standard Model.
The basic idea is that somehow (we don’t know how) Nature is able to blindly stumble into repetitive behavior and acquire habits. That Nature has something analogous to an associative memory of its own past behavior.
I see no qualitative difference between assuming that (if one can formulate it clearly) and assuming Newton’s Laws of Motion. It’s just that we are used to Newton’s laws.

The problem I see for Smolin and collaborators would be with formulation. It is similar to the difficulty of programming artificial intelligence, one must be able to make a toy model of Nature that uses a *similarity* criterion for recognizing the similar past situations which would constitute precedents to be sampled randomly. It seems similar to the AI problem of programming an *associative memory* to use in constructing some almost completely unintelligent habit-forming automaton.

Newton explained his absolute space and time as Sensorium Dei. That was weirder than this, or so I think anyway. Basically it is a fun idea whose time is come. Hopefully they can make a toy model work and actually generate some law-like patterns of behavior.

“What if you had two or more totally causally disconnected universes: would they need to share a global notion of simultaneity with each other?”

I think yes! Lee’s rhetorical resp0nse — “What do you mean that they keep up with each other? Isn’t that a global time?” — agrees, yet I think more needs to be said about what “causally disconnected” means. In Einstein’s relativity, simultaneous though relativistically separated events are causally disconnected; multiple universes sharing a boundary and also sharing simultaneously branching binary events make Smolin’s “real time” proposition even more attractive. Given, as Wheeler noted, “The boundary of a boundary is zero,” spatial boundaries do not obviate analytical continuation of the time metric — as I have found, general relativity suffers no loss of generality when described as a model bounded in space and unbounded in time (rather than, as conventionally thought, bounded in time at the singularity of creation and unbounded in space).

That is an excellent question and one that I am focusing on as I try to develop the hypothesis of precedence further. As formulated in the original paper arXiv:1205.3707 I just assume it does so. What intrigues me is that the question of how precedence develops might be investigated experimentally by studying quantum systems complex enough to have no natural precedents. Nor is it necessary to have a detailed model of how precedence develops to test for deviations from the expected Schroedinger evolution in such cases.

Let me stress that this idea, like CNS, doesn’t have to be right to prove the point that theories of evolving laws are testable and hence at least as scientific as the claim that laws never evolve-which leads to attempts to explain the choices of laws that have no testable consequences.

Thank you for your earlier correction; I re-checked the relevant slide and saw that I had misread it.

One warning/heads up: The notion of laws evolving as the universe gains “experience,” and your ideas about precedence bear a superficial resemblance to the concept of “morphogenetic fields” propounded by Rupert Sheldrake. He has argued for example, that when one lab gets a certain chemistry experiment to work then all future versions of that experiment at other labs are more likely to work. His ideas have the flavor of the paranormal and attract those who are sympathetic to such things. You might want to be prepared with a response in the not unlikely event that your work is cited in support of his theories.

I would like to ask Lee the following question, if he is still checking this blog for discussion and wishes to respond. Can you imagine a precedence process by which the quantum theory called Causal Dynamical Triangulations arises?

CDT has a preferred time or at least a preferred foliation, and is built up in layers with a certain thickness.
(This resembles what was described in the February seminar talk.)
And there is a certain random probabilistic process that governs the formation of the each layer (based on a Regge-like partition function). That could be seen as similar to “sampling from the past” in the precedence process—though not identical by any means! So I can just barely imagine how something like CDT might arise through geometric habit-formation. I’d like to know what other people (Lee in particular) think about this.

Here is Chris Kennedy’s 5star review on Amazon of Smolin’s book.http://www.amazon.com/review/R2F83657IVWFJ9
If you happen to read it and find it helpful consider clicking the accompanying “yes” button, because something like Smolin’s metalaw operates at Amazon. Customer reviews that don’t get noticed and don’t acquire “yes this was helpful” votes stay at the bottom of the pile and may not ever get noticed and yessed enough to rise the top of the pile where people see them.

Right now the top of the pile of “customer” reviews is all composed of quite disagreeable 2star reviews and the like. It appears that visitors see the half dozen negative reviews, mark them as helpful, if for no other reason than because they help one decide not to delve further and take any further interest in the book. So unless you are experienced it’s actually a bit difficult to even FIND Chris Kennedy’s review (which only 8 people have approved of so far).

Marcus,
Thanks for posting the link that goes directly to the review and my comment below the review. I wanted to make people aware that part of my criticism I originally offered was a little reckless when I said: “he didn’t specifically explore how time dilation (during relative motion and proximity to mass) fit in with a real, global theory of time” and after Lee straightened me out on the applications of shape dynamics, I posted the correction. However, as someone who is interested in the nuts and bolts of the nature of time, any theory for how and why time dilates deserves much more discussion and clarification. Putting all of our eggs in the shape dynamics basket might be too simple of a path to take at this point.